VOLUME FIFTY NINE PROGRESS IN OPTICS EDITORIAL ADVISORY BOARD G.S Agarwal Stillwater, USA T Asakura Sapporo, Japan M.V Berry Bristol, England C Brosseau Brest, France A.T Friberg Joensuu, Finland F Gori Rome, Italy D.F.V James Toronto, Canada P Knight London, England G Leuchs Erlangen, Germany P Milonni Los Alamos, NM, USA J.B Pendry London, England J Perˇina Olomouc, Czech Republic J Pu Quanzhou, PR China W Schleich Ulm, Germany T.D Visser Amsterdam, The Netherlands VOLUME FIFTY NINE PROGRESS IN OPTICS Edited by E WOLF University of Rochester, NY, USA Contributors Maria L Calvo, Natalie A Cartwright, Pavel Cheben, Radim Chmelik, Jana Collakova, Zbynek Dostal, Mirosław Florjańczyk, Ortwin Hess, Vera Kollarova, Martin Lostak, Kurt E Oughstun, Jan Peřina Jr., Michala Slaba, Tomas Slaby, Aitor V Velasco, Sebastian Wuestner Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo Elsevier The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK Radarweg 29, PO Box 211, 1000 AE Amsterdam, The Netherlands First edition 2014 Copyright © 2014, Elsevier B.V All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher Permissions may be sought directly from Elseviers Science & Technology Rights Department in Oxford, UK: phone (+44) (0) 1865 843830; fax (+44) (0) 1865 853333; email: permissions@elsevier.com Alternatively you can submit your request online by visiting the Elsevier web site at http://elsevier.com/locate/permissions, and selecting Obtaining permission to use Elsevier material Notices No responsibility is assumed by the publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-444-63379-8 ISSN: 0079-6638 For information on all Elsevier publications visit our website at store.elsevier.com Printed and bound in Great Britain 14 15 16 17 11 10 CONTRIBUTORS Maria L Calvo Department of Optics, Faculty of Physical Sciences, Complutense University of Madrid, 28040 Madrid, Spain Natalie A Cartwright Department of Mathematics, State University of New York, New Paltz, NY 12561, USA Pavel Cheben National Research Council Canada, Ottawa, Canada K1A 0R6 Radim Chmelik CEITEC – Central European Institute of Technology, Brno University of Technology, Technicka 10, Brno 616 00, Czech Republic Institute of Physical Engineering, Brno University of Technology, Technicka 2, Brno 616 00, Czech Republic Jana Collakova CEITEC – Central European Institute of Technology, Brno University of Technology, Technicka 10, Brno 616 00, Czech Republic Institute of Physical Engineering, Brno University of Technology, Technicka 2, Brno 616 00, Czech Republic Zbynek Dostal CEITEC – Central European Institute of Technology, Brno University of Technology, Technicka 10, Brno 616 00, Czech Republic Institute of Physical Engineering, Brno University of Technology, Technicka 2, Brno 616 00, Czech Republic Mirosław Florjan´czyk National Research Council Canada, Ottawa, Canada K1A 0R6 Ortwin Hess The Blackett Laboratory, Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom Vera Kollarova CEITEC – Central European Institute of Technology, Brno University of Technology, Technicka 10, Brno 616 00, Czech Republic Martin Lostak Institute of Physical Engineering, Brno University of Technology, Technicka 2, Brno 616 00, Czech Republic Kurt E Oughstun College of Engineering and Mathematics, University of Vermont, Burlington, VT 05401, USA v vi Contributors Jan Perˇina Jr Institute of Physics of Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University, 17 listopadu 12, Olomouc 772 07, Czech Republic Michala Slaba CEITEC – Central European Institute of Technology, Brno University of Technology, Technicka 10, Brno 616 00, Czech Republic Institute of Physical Engineering, Brno University of Technology, Technicka 2, Brno 616 00, Czech Republic Tomas Slaby Institute of Physical Engineering, Brno University of Technology, Technicka 2, Brno 616 00, Czech Republic Aitor V Velasco Department of Optics, Faculty of Physical Sciences, Complutense University of Madrid, 28040 Madrid, Spain Sebastian Wuestner The Blackett Laboratory, Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom PREFACE This volume of Progress in Optics presents five review articles on the following subjects: Active optical metamaterials, spontaneous parametric down-conversion in nonlinear layered structures, spatial heterodyne Fourier-transform waveguide spectrometers, precursors and dispersive pulse dynamics, and the role of coherence in image formation in holographic microscopy Both theoretical and experimental aspects of these subjects are discussed Emil Wolf Department of Physics and Astronomy and The Institute of Optics University of Rochester Rochester, NY 14627, USA January 2014 ix CHAPTER ONE Active Optical Metamaterials Sebastian Wuestner and Ortwin Hess The Blackett Laboratory, Department of Physics, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom Contents Introduction Nanoplasmonic Metamaterials 2.1 Plasmonics: Optics on the Nanoscale 2.1.1 2.1.2 2.1.3 2.1.4 8 Electromagnetic Fields in Media: Maxwell’s Equations Dispersive Response Models Plasmons on the Surface of Metals Time-Domain Description of Surface Plasmons 10 11 14 2.2 Metamaterials: Control of the Flow of Light on the Nanoscale 17 2.2.1 Effective Electric Metamaterials 2.2.2 Effective Magnetic Metamaterials 2.2.3 Extraction of Effective Parameters 2.3 Negative Refractive Index Metamaterials 2.4 The Double-Fishnet Metamaterial 2.5 Losses in Nanoplasmonic Metamaterials Optical Gain Media in Nanoplasmonics 3.1 Comparison of Optical Gain Media 3.2 Laser Dye Gain Media 3.3 Full Time-Domain Optical Maxwell-Bloch Equations 3.3.1 Optical Bloch Equations for Two-Level Systems 3.3.2 Semiclassical Maxwell-Bloch Equations for Four-Level Systems Loss Compensation in a Nanoplasmonic Negative Refractive Index Metamaterial 4.1 Optical Properties of Passive Double-Fishnet Metamaterials 4.2 Active Double-Fishnet Metamaterial 4.3 Inhomogeneous Deposition of Gain 4.4 The Probe Process: Plasmonic Resonator with Gain 4.5 Effective Parameters of the Loss-Compensated Double Fishnet 4.6 Summary Nonlinear Dynamics of Bright and Dark Lasing States 5.1 Bright and Dark Modes 5.2 Ultra-Fast Relaxation Oscillations 5.3 Nonlinear Mode Competition Progress in Optics, Volume 59 © 2014 Elsevier B.V ISSN 0079-6638, http://dx.doi.org/10.1016/B978-0-444-63379-8.00001-5 All rights reserved 18 20 22 25 28 32 34 34 36 38 38 41 45 47 53 55 58 60 64 65 67 70 74 Sebastian Wuestner and Ortwin Hess 5.4 Threshold Behavior 5.5 Methods for Mode Control 5.6 Summary Conclusion and Outlook Acknowledgments References 77 78 81 82 83 83 INTRODUCTION At the turn of the century, a new field of research emerged at the crossing between physics, electrical engineering, and materials science The study of metamaterials addresses the rational design and arrangement of a material’s building blocks to attain physical properties that may go significantly beyond those of its original constituent materials Most often, the concept of metamaterials is associated with electromagnetic wave propagation, where the engineering of resonant subwavelength structures allows for the precise control of effective wave properties It is this advanced functionality that enables the realization of unique wave phenomena, such as the focusing of light below the diffraction limit or electromagnetic cloaking of objects— concepts that have captured the imagination of researchers and the general public alike Importantly, the element of functionality is an integral part of the metamaterial concept Pioneering work by Pendry in 1996 showed that a medium composed of parallel thin metallic wires would allow for a tuning of its electromagnetic response by changes to the diameter of the wires or their spacing (Pendry, Holden, Stewart, & Youngs, 1996) Functionality in this wire-mesh (WM) medium is thus derived from structural parameters, making it one of the first metamaterials conceived Yet this work is closely connected with earlier research in electrical engineering in the 1950s on “artificial dielectrics,” where the engineering of effective electromagnetic properties at microwaves and longer wavelengths enabled the realization of lightweight, metallic delay lenses (Milonni, 2005) It was also realized at the time that an effective diamagnetic response could arise from the interaction of electromagnetic waves with the metallic subwavelength building blocks of these lenses In a breakthrough study in 1999, Pendry demonstrated that the design flexibility of metamaterials enables the realization of structures that exhibit artificial magnetism strong enough to give rise to negative permeability (Pendry, Holden, Robbins, & Stewart, 1999) Original design proposals included the Swiss roll and the split ring resonator (SRR) structure, with cell sizes of the order of mm operating at wavelengths of 10 cm in the microwave regime The functionality of the metallic SRR building blocks derives from Active Optical Metamaterials the inductive and capacitive response of free charges and currents in terms of inductive-capacitive resonant loops The SRR structure in particular proved to be a seminal design in achieving artificial magnetism across the electromagnetic spectrum (Linden et al., 2004; Soukoulis, Linden, & Wegener, 2007) The unprecedented control over electromagnetic properties provided by metamaterials (Smith, Pendry, &Wiltshire, 2004) revived a reconsideration of initially rather academic studies discussed 30 years earlier by Veselago (1968), Mandelstham, and other renowned scientists (Shalaev, 2007) In those early works, the effects of simultaneous negative permittivity and permeability on wave propagation were investigated and it was predicted that electromagnetic properties would be described by a negative refractive index (NRI) As the refractive index enters most fundamental equations of optics, important physical laws, originally derived for “normal” positive refractive index (PRI) materials, had to be reviewed and fundamental assumptions re-visited For example, the flow of energy in a NRI material opposes the direction of the phase advance, i.e., the Poynting vector and the wavevector point in opposite directions (Veselago, 1968) This property is also associated with the remarkable fact that Snell’s law predicts negative refraction of a beam of light at the interface between PRI and NRI materials As a result, the role of convex and concave lenses on the focusing of plane waves interchanges However, this is not the most exciting property of NRI lenses In 2000, it was predicted that an NRI material with permittivity and permeability equal to negative unity would provide the basis for a realization of a “perfect lens” (Pendry, 2000); a lens with imaging resolution that is not diffraction-limited to half the operating wavelength Indeed, much momentum and excitement in the field of metamaterials originated from this possibility of subwavelength imaging Yet no less intriguing is the prediction of broadband “stopped light” (the “trapped rainbow”) in a simple waveguide heterostructure exploiting negative phase shifts in structures combining PRI and NRI or plasmonic waveguide materials (Tsakmakidis, Boardman, & Hess, 2007) Another application of metamaterials, which, however, does not necessarily rely on negative refractive index, is the control of the flow of light by gradient index structures in terms of transformation optics (Pendry, Schurig, & Smith, 2006) Transformation optics has, for example, delivered the blueprint for a realization of a metamaterial cloak, which guides light around an electromagnetically forbidden region (Schurig et al., 2006) In the same year in which the concept of the perfect lens was formulated, Smith and co-workers documented the first demonstration of a metamaterial ... imaging Yet no less intriguing is the prediction of broadband “stopped light” (the “trapped rainbow”) in a simple waveguide heterostructure exploiting negative phase shifts in structures combining... from inductive-capacitive inclusions was composed of cells containing pairs of concentric split ring resonators (SRR) (Pendry et al., 1999) Split ring resonators are open metallic rings (thin rings... is due to an inductance-like term stemming from the imaginary part of the conductivity, which can be interpreted as a kinetic inductance Lk and adds to the total self-inductance L In comparison